Difference between revisions of "Store:FLen02"

Latest revision as of 15:03, 13 March 2023

Fuzzy truth

In the ambitious attempt to mathematically translate human rationality, it was thought in the mid-twentieth century to expand the concept of classical logic by formulating fuzzy logic. Fuzzy logic concerns the properties that we could call ‘graduality’, i.e., which can be attributed to an object with different degrees. Examples are the properties ‘being sick’, ‘having pain’, ‘being tall’, ‘being young’, and so on.

Mathematically, fuzzy logic allows us to attribute to each proposition a degree of truth between $0$ and $1$ . The most classic example to explain this concept is that of age: we can say that a new-born has a ‘degree of youth’ equal to $1$ , an eighteen-year-old equal to $0,8$ , a sixty-year-old equal to $0,4$ , and so on

In the context of classical logic, on the other hand, the statements:

- a ten-year-old is young
- a thirty-year-old is young

are both true. However, in the case of classical logic (which allows only the two true or false data), this would mean that the infant and the thirty-year-old are equally young. Which is obviously wrong.

The importance and the charm of fuzzy logic arise from the fact that it is able to translate the uncertainty inherent in some data of human language into mathematical formalism, coding ‘elastic’ concepts (such as almost high, fairly good, etc.), in order to make them understandable and manageable by computers.

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-==Fuzzy Wahrheit==
+==Fuzzy truth==
-In dem ehrgeizigen Versuch, die menschliche Rationalität mathematisch zu übersetzen, dachte man Mitte des 20. Jahrhunderts daran, den Begriff der klassischen Logik durch die Formulierung der Fuzzy-Logik zu erweitern. Die Fuzzy-Logik betrifft die Eigenschaften, die wir als „Gradualität“ bezeichnen könnten, d. h. die einem Objekt mit unterschiedlichen Graden zugeschrieben werden können. Beispiele sind die Eigenschaften „krank sein“, „Schmerzen haben“, „groß sein“, „jung sein“ und so weiter.
+In the ambitious attempt to mathematically translate human rationality, it was thought in the mid-twentieth century to expand the concept of classical logic by formulating fuzzy logic. Fuzzy logic concerns the properties that we could call ‘graduality’, i.e., which can be attributed to an object with different degrees. Examples are the properties ‘being sick’, ‘having pain’, ‘being tall’, ‘being young’, and so on.
-Mathematisch erlaubt uns die Fuzzy-Logik, jeder Aussage einen Wahrheitsgrad zwischen <math>0</math> und <math>1</math> zuzuschreiben. Das klassischste Beispiel zur Erklärung dieses Konzepts ist das Alter: Wir können sagen, dass ein Neugeborenes einen „Jugendgrad“ hat, der gleich ist <math>1</math>, ein Achtzehnjähriger gleich <math>0,8</math>, ein Sechzigjähriger gleich <math>0,4</math> und so weiter
+Mathematically, fuzzy logic allows us to attribute to each proposition a degree of truth between <math>0</math> and <math>1</math>. The most classic example to explain this concept is that of age: we can say that a new-born has a ‘degree of youth’ equal to <math>1</math>, an eighteen-year-old equal to <math>0,8</math>, a sixty-year-old equal to <math>0,4</math>, and so on
-Im Kontext der klassischen Logik hingegen gelten die Aussagen:
+In the context of classical logic, on the other hand, the statements:
-**ein Zehnjähriger ist jung
+**a ten-year-old is young
-**ein Dreißigjähriger ist jung
+**a thirty-year-old is young
-sind beide wahr. Im Fall der klassischen Logik (die nur die beiden wahren oder falschen Daten zulässt) würde dies jedoch bedeuten, dass der Säugling und der Dreißigjährige gleich jung sind. Was offensichtlich falsch ist.
+are both true. However, in the case of classical logic (which allows only the two true or false data), this would mean that the infant and the thirty-year-old are equally young. Which is obviously wrong.
-Die Bedeutung und der Charme der Fuzzy-Logik ergeben sich aus der Tatsache, dass sie in der Lage ist, die Unsicherheit, die einigen Daten der menschlichen Sprache innewohnt, in mathematischen Formalismus zu übersetzen und „elastische“ Konzepte (wie fast hoch, ziemlich gut usw.) zu codieren um sie für Computer verständlich und handhabbar zu machen.
+The importance and the charm of fuzzy logic arise from the fact that it is able to translate the uncertainty inherent in some data of human language into mathematical formalism, coding ‘elastic’ concepts (such as almost high, fairly good, etc.), in order to make them understandable and manageable by computers.